Asset Pricing Equation Research Articles

Intermediary Capital and the Credit Market

We propose a tractable framework to examine the role of intermediary capital in the allocation and pricing of credit. In our model, regulated financial intermediaries compete with unregulated investors, targeting distributions of heterogeneous borrowers. We derive a sufficient statistic that characterizes intermediaries’ cross-sectional lending decisions and provide a novel intermediary asset pricing equation that accounts for the endogenous segmentation of marginal investors across securities. These formulae reveal the central role of intermediaries’ shadow cost of capital in both credit allocation and pricing. Our results can concurrently rationalize a broad array of empirical facts documented in the context of credit markets. This paper was accepted by Tomasz Piskorski, finance. Funding: This work was supported by Marcus och Amalia Wallenbergs minnesfond [Grant 2021.0122].

Three Remarks On Asset Pricing

The consideration of an averaging interval Δ of market trade time-series change the basic consumption-based asset pricing equation. The duration of Δ determines Taylor series of investor’s utility over current and future values of consumption. We present consumption at current and future moments as sums of their mean values and perturbations during Δ of the price at current moment t and perturbations of the payoff at day t+1. Linear and quadratic Taylor series approximations of the basic equation describe new relations on mean price, mean payoff, their volatilities, skewness and amount of asset ξmax that delivers max to investor’s utility. The stochasticity of market trade time-series defines the randomness of the asset price. We introduce the new price probability measure entirely determined by the probability measures of market trade value and volume. The conventional frequency-based price probability is a special case of the new price probability measure when all trade volumes during the averaging interval Δ equal unit. Prediction of the price probability measure at horizon T equals forecasts of the market trade value and volume probabilities at same horizon.

Asset Pricing with Price Levels

We propose a novel way to study asset prices based on price distortions rather than abnormal returns. We derive the correct identity linking current mispricing to subsequent returns, generating a price-level analogue to the fundamental asset pricing equation, E[MR^e]=0, used to study returns. Our empirical test reveals that the CAPM describes the cross-section of prices better than it describes expected short-horizon returns. Despite the improvement, significant mispricing remains. An interaction of book-to-market and quality provides a parsimonious model of CAPM mispricing that both long-term buy-and-hold investors and researchers disciplining models from the price perspective should prioritize.

The role of household debt and delinquency decisions in consumption-based asset pricing

I incorporate household debt and delinquency decisions into a standard model of lifecycle consumption-saving-investment. I also impose a punishment to the delinquent behavior by assuming that the percentage of endowment available is a linear function of the default decision. Theoretically such additional investor decisions are playing a relevant role in terms of completing markets. In practice, it enables me to derive an extended system of Euler equations which does not alter consumption-based fundamental asset pricing equation. It imposes the pricing kernel to account jointly for two additional first-order conditions. I perform empirical exercises aiming to price equity premium in United States from 1987:1 to 2018:1. I find significant elasticity of intertemporal substitution in consumption of the representative agent ranging from 0.24 to 0.55 and risk aversion from 1.82 to 3.51. This approach is also useful to account for the cross-section behavior of domestic assets. I can also use this framework to draw bounds for the household decisions on loan and delinquency and to propose a new rule of thumb relating preferences parameters and credit variables.

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The state-dependent time variation in the value premium

It is well documented that asset and strategy returns are generally exposed to identifiable risk factors. Moreover, the exposure to these systematic risk factors tends to be time varying. Examples of strategies that exhibit such regime-dependent variability include value investing in equity markets and carry in foreign exchange markets. The literature proposes several macro-based explanations for this time variation such as liquidity or cyclicality risk depending on the strategy and horizon under consideration. This project relies on developments in the academic literature in the area of state-dependent asset pricing models (see, for example, survey by van Dijk et al, 2002). Under such a framework, a strategy return is modelled using a multi-factor asset pricing equation where the risk sensitivities (or betas) to the pre-defined factors are allowed to vary according to one or multiple state variables. The approach considered here uses a logistic smooth transition regression methodology applied to the value strategy, where the state variables have an economic meaning (see Christiansen et al, 2011 application to foreign exchange carry strategy). By distinguishing between low and high state regimes (in a continuous space), the aim is to first investigate improvements in the explanatory power of the model relative to the linear (no-state dependency) approach. In particular, we study the performance of the value factor during turbulent periods, and identify economic variables driving its time-varying behaviour. We also present an algorithm that allocates dynamically to a long–short value overlay portfolio conditioned on regime transitions. We show that the performance of this dynamic portfolio is superior to a portfolio with a static value overlay.

Safety First, Robust Dynamic Asset Pricing, and the Cross-Section of Expected Stock Returns

We investigate the implications of investors’ aversion to Knightian uncertainty for the cross-section of average stock returns. First, we derive the fundamental dynamic asset pricing equation in beta regression form of a robust investor concerned with Knightian uncertainty. Second, we provide empirical evidence that learning and uncertainty are both risk dimensions of systematic risk priced in the cross-section of stock returns. However, the risk premium component corresponding to uncertainty dominates the one corresponding to learning as investors’ investment horizon increases. Third, we report that a robust version of the intertemporal CAPM (ICAPM) explains average stock returns better than the four-factor model and the standard ICAPM.

Expected Returns and Liquidity Risk: Does Entrepreneurial Income Matter?

This paper studies the effects of jointly incorporating liquidity risk and non-tradeable wealth in a single asset pricing equation. First, I propose an overlapping-generations model with random endowment shocks and liquidity risk, evaluating their joint impact on expected returns. The model presents a single-factor asset pricing equation, with a new term capturing the covariance between assets' liquidities and non-tradeable wealth. In this economy, assets with higher liquidity or returns when non-tradeable wealth is low command lower expected returns. Second, I investigate whether risks associated with liquidity are priced after including non-tradeable wealth due to entrepreneurial income. I test the model on equally weighted and value-weighted portfolios, sorted by illiquidity levels, illiquidity variation and size, using US stock data from January 1962 to December 2004. The extra terms due to entrepreneurial income reduce liquidity risk premium by almost 40%, with an impact of -0.45% per year on expected returns of value-weighted illiquidity-sorted portfolios. Overall, liquidity risk as a whole has a yearly premium equal to 1.06%. However, liquidity levels are much more important and have a premium of 6.14% per year, contributing to most of the explanatory gains of the model.

Episodic Liquidity Crises: Cooperative and Predatory Trading

ABSTRACTWe describe how episodic illiquidity arises from a breakdown in cooperation between market participants. We first solve a one‐period trading game in continuous‐time, using an asset pricing equation that accounts for the price impact of trading. Then, in a multi‐period framework, we describe an equilibrium in which traders cooperate most of the time through repeated interaction, providing apparent liquidity to one another. Cooperation breaks down when the stakes are high, leading to predatory trading and episodic illiquidity. Equilibrium strategies that involve cooperation across markets lead to less frequent episodic illiquidity, but cause contagion when cooperation breaks down.

Expected Returns and Liquidity Risk: Does Entrepreneurial Income Matter?

This paper studies the effects of jointly incorporating liquidity risk and non-tradeable wealth in a single asset pricing equation. First, I propose an overlapping-generations model with random endowment shocks and liquidity risk, evaluating their joint impact on expected returns. The model presents a single-factor asset pricing equation, with a new term capturing the covariance between assets' liquidities and non-tradeable wealth. In this economy, assets with higher liquidity or returns when non-tradeable wealth is low command lower expected returns. Second, I investigate whether risks associated with liquidity are priced after including non-tradeable wealth due to entrepreneurial income. I test the model on equally weighted and value-weighted portfolios, sorted by illiquidity levels, illiquidity variation and size, using US stock data from January 1962 to December 2004. The extra terms due to entrepreneurial income reduce liquidity risk premium by almost 40%, with an impact of -0.45% per year on expected returns of value-weighted illiquidity-sorted portfolios. Overall, liquidity risk as a whole has a yearly premium equal to 1.06%. However, liquidity levels are much more important and have a premium of 6.14% per year, contributing to most of the explanatory gains of the model.

Asset Pricing Model With Stopping Option and Entering Option: Intelligent Arbitrage Pricing Theory

There are many anomalies beyond the explanation capacity of CAPM and APT. In their asset pricing models with heterogeneous agents, Miller and his successive researchers shed some lights on the effects of trading, but they only analyze the behavior of stock owners, neglecting the behavior of owners of risk-free assets(say government bonds). Without the assumption of short sale constraints and irrational behavior, we provide a new model with heterogeneous beliefs due to new information, by including effects of speculative behavior of both stock owners and bond owners. Significantly different to existing models, our asset pricing equation connects the asset price with the new information, turnover and relative quantity of the asset to the risk-free bond. Our model provides an explanation for the overvaluation and undervaluation of the asset price, and implies that an the relative quantity of stocks to bonds plays a key role in the evolution process of the stock price. In our model, overvaluation is not a negative and useless so-called price bubble, but the rewards to exploring uncertainty. Illustrated in the case of the rise and crash of the 90's internet boom, an effective policy is provided to ease the volatility of asset prices, that is, government should stabilize the quantity of the government bonds and relax the regulation of the financial market to facilitate the adjustment of the quantity of financial assets in the market.

Exploring consumption-based asset pricing model with stochastic-trend forcing processes

Using Canadian data, the consumption-based asset pricing model is studied, defined in terms of nondurable and durable goods consumption. A two-stage estimation procedure is used, which takes account of the presence of common stochastic trends in the forcing processes. This method yields more reasonable estimates of the preference parameters than the previous studies did, and the asset-pricing equation is not rejected by the data. Moreover, the preference specification adopted in this paper allows a number of useful economic information to be obtained. The additive separability assumption and the Cobb–Douglas functional form of the utility function are ruled complements in the sense of Edgeworth and Pareto.

An Asset Pricing Model with Time-varying Elasticity of Intertemporal Substitution

The main message of this paper is that it is Elasticity of Intertemporal Substitution, which is at the heart of the asset pricing puzzles, not Risk Aversion. We illustrate that point, by first showing that under certainty a model, which allows for a separation of the two characteristics of preferences - the one in Epstein and Zin (1991), leads to a specification of the main pricing equation, which involves a measure of Elasticity of Intertemporal Substitution only and not a measure of Risk Aversion. We then resort to an approximation of the main asset pricing equation under uncertainty, to demonstrate the central role played by Elasticity of Intertemporal Substitution and to emphasize the importance of its variability. We illustrate that importance by showing that the model in Campbell and Cochrane (1999) is in fact based on time-varying Elasticity of Intertemporal Substitution rather then on time-varying Risk Aversion. The main contribution of the paper is to develop a discrete-time alternative to the two most popular recursive utility based asset pricing models. The model proposed in the paper, directly nests the standard one, while replicating and improving upon the two frequently cited advantages of the Epstein-Zin model. It allows for time-varying risk premia, associated with the two most popular asset pricing factors and it achieves separation of risk attitudes from attitudes towards time via constant relative risk aversion (CRRA) and time-varying Elasticity of Intertemporal Substitution.

On The Use of Elasticity of Intertemporal Substitution

Our main message is that it is Elasticity of Intertemporal Substitution (EIS), which is at the heart of asset pricing puzzles, rather than Risk Aversion. An approximation of the main asset pricing equation demonstrates that central role and allows us to show that the Campbell-Cochrane model produces wide range of mean equity premia, because it uses time-varying EIS. The paper introduces a complete-markets consistency check, which applied to the Epstein-Zin model allows us to estimate the parameter EIS over different horizons. We conclude that EIS should be used (modelled and thought of) as a variable, rather than as a parameter.

Review of John Cochrane's 'Asset Pricing'

John Cochrane's Asset Pricing (2001, Princeton University Press) is targeted at economics and finance Ph.D. students, advanced MBA students, or professionals with similar background. Residing in the third camp, I can say from this point of view that Asset Pricing could have been subtitled, the Practitioner's Portable Ph.D. Academic researchers, students, and practitioners of finance should all value Cochrane's Asset Pricing enough to own a copy. The book is extremely readable, as Cochrane stresses economic intuition over formal proofs. It is structured into four parts: 1) asset pricing theory; 2) asset pricing models; 3) options and interest rates; 4) an empirical survey. Cochrane begins powerfully, introducing us to the notion that the consumption-based asset pricing equation, given by an investor's first-order conditions, is the central formulation in asset pricing; market-based models simply consider the market returns specified in the consumption models to be exogenously determined free parameters. In Part 1, Cochrane covers the field from the Law of One Price, to the mean-variance frontier, to the CCAPM, the CAPM, ICAPM and APT, covering both discrete- and continuous-time, as well as market- and consumption-oriented approaches. Part 2 introduces us to The Generalized Method of Moments (GMM) approach to free parameter selection, distribution estimation, and model evaluation. In Part 3, Cochrane covers option pricing and term structure of interest rate models. Part 4 provides a well-written survey of the empirical work in the field, specifically on time-series predictability, cross-sectional models and equity premium puzzles, and new variations on the consumption-based models. Most chapters include several problems at the end, a nice addition for readers who really want to dig in and explore asset pricing directly. Although solutions are not provided in the book, Cochrane's website offers them via e-mail to teachers using Asset Pricing as a class text. The website also offers a preview of the book through page 50, which encompasses the Contents, Preface, and chapters 1 and 2 in their entirety. The website also contains an important errata page describing more than 160 equation typos and errors, additions and clarifications to the manuscript. Cochrane's experience as editor of the Journal of Political Economy shines through in his clear writing style, and his students at Chicago's GSB, where he is Theodore O. Yntema Professor of Finance, are lucky indeed if this book is any indication of his teaching ability. Asset Pricing is not a book to be missed.

Re-Examining Variance-Bounds Tests for Asset Prices

The hypothesis of market efficiency is typically rejected by standard variance-bounds tests which assume stationary asset prices. A number of researchers, however, argue that tests used in previous studies are inappropriate since asset prices appear to be generated by nonstationary processes. In this paper, we propose a regression-based variance-bounds test that is valid when the asset price is an integrated process. We apply this test to annual U.S. data over the 1889 to 1985 sample period using measures of the perfect-foresight price constructed from a nonlinear asset-pricing equation that allows for a stochastic discount parameter. The results suggest that the data appear consistent with a version of the efficient-market hypothesis detailed in this paper.

On Cash-in-Advance Models of Money Demand and Asset Pricing

This paper shows how a cash-in-advance model of money can be written in a way that combines a simple, yet empirically defensible, money demand function with an asset pricing equation that is similar to the standard barter-economy Euler equations. Return premia are determined as in the barter exchange model, except that a short-term, risk-free, nominal interest rate enters into the first-order conditions. In special cases, asset prices satisfy the barter-economy Euler equations exactly. In the empirical analysis, the interest rate factor adds some explanatory power, but both the barter and the monetary asset pricing model perform rather poorly. Copyright 1991 by Ohio State University Press.